Riddles in Translation - (For Wed Sept 23rd)

Why is a raven like a writing desk?

That riddle is just about as confusing to me as a Babylonian word problem, but I suppose one of them is supposed to make sense. I see nonsense, and a Babylonian scholar would see a simple word problem which merely has to be worked out, but it's supposed to be simple, right? Well the modern version of solving the algebraic equation is very simple and fun to me, but I can't make sense at all of the Babylonian way of doing things. I'm sure they have a standard way of working through the problems, an algebra of their own which doesn't really resemble ours. Unfortunately, my unfamiliarity with their methods and language to describing problems makes it feel like an untranslated riddle, even though it's already in English. When we're unfamiliar with the language and rules of something new, it can seem like it's in a foreign language. I'd argue that this experience is common among many students who are first introduced to algebra. As such, we should be quite empathetic and patient with students when they're first encountering algebra. The real question is, how do we introduce algebra in a way that is easily understandable to students? 

So why is a raven like a writing desk? I haven't the slightest idea, but I hope to learn.

The Unfortunate Timing of Time - (For Mon Sept 21st)

The time has come!

I've honestly never really thought about time too seriously. We learn about the four seasons, the 12 months, the 12 hours. I simply accepted the information for the way it is. What I find more fascinating is that the day and night were seen as two separate entities. So as the total amount of hours of daylight changed, so did the length of the hour. I find it would be incredibly confusing trying to keep track of the 12 hours of the day, but having the length of each hour change throughout the season. Did the people of older times precisely understand the time of the day, and intuitively understand the length of the hour as it changed throughout the season , or did they just accept this way of time because laymen didn't keep track of it very precisely? Simply divide the day into 12 equal parts, and that's how the hours pass. I suppose there is the advantage that 6 hours into the day is always the middle of the day, always at the apex of the sun. At that point I think I would just have the understanding that it's either the morning, close to the 6 hour mark, close to after the 6 hour mark, and then close or the end of the day. Perhaps that's why we divided up days so simply, it's either the morning, afternoon, or evening, which follows my idea if you are to choose the 6 hour mark to be noon. I am really fascinated by the water clock, mostly because it kept track of time so accurately and throughout all times, even at night. People of today's age, at least our society, have a deep connection to the accuracy of time. We keep track of the majority of events down to the minute. Class starts on time, it has a fixed amount of time, we have a fixed time between our next class, assignments are due at specific times, exams are times, etc. Thus as someone from today's age I am dawn immediately to the accuracy of the water clock. I'm sure the designers of such clock also had a deep interest in keeping track of time, but I imagine the majority of people cared not for it's design and purpose. I would go even further to say that I the majority of people rejected the idea outright. Looking back at history there was a huge pushback by humans against the imposition of clocks and standardized time. It's fascinating how time became to be the way it is, but perhaps human's would be happier if time was never standardized.

Well anyway, the time has come, my little friends, to talk of other things! 

Math in Motion - Base 60, 45 multiplication table

Math in motion, as it was done on the bus

The Historical Circulations of Mathematical Information & Ideas

Round and round the knowledge goes, where it stops, Europe knows.

 Before my introduction into university classes I wouldn't have known that mathematics came from all kinds of different cultures, and how some discoveries happened multiple times or simultaneously if different places. Thankfully I was already given this perspective by this point in my learning journey. However, I had no understanding of how much mathematicians moved around in their pursuit of knowledge. Not only would travel have been dangerous and slow during the time periods, but they would have had to learn completely new languages upon arriving at their new epicenter of discovery. My brain always just envisioned the flow of information, never considering the people who had to carry, translate, teach, and learn it. I'm quite surprised at the risks people took to continue and expand their knowledge of mathematics. 

Another great thing I didn't particularly think about was the fall of nations and their mathematical institutions. This fact probably drove my first surprise in how mathematicians moved around so much. On top of that, all the effort and work of mathematicians and historians to keep the collections of information of these civilizations and institutions that fell. The history of mathematics tells a great tale of the efforts of individuals and institutions to preserve, learn, advance mathematics through the ages. I can only wonder the amount of knowledge that was lost through time.

Ingredients to the Pocketwatch of Mathematics

 

 

Arithmetic, Algebra, Geometry, Logic, History. 

HISTORY?! Don't let's be silly!

We really can't compare history to mustard in our pocket watch of mathematics. Unlike mustard, I do believe there is a place for history in math. 

1) I think history should be incorporated into teaching mathematics, for the history of math is a subject area of math. Learning it could provide a fuller understanding of math, it may interest some students and provide engagement, and it adds a slight variety to classroom learning. How it should be added is not as clear to me. My only current thought would be little snippets in the lesson plan to add some interesting history and background.

2) The article had a confusing pitch. I expected to be more convinced, but it made some really strong points about why history shouldn't be added to math. The article attempted to counter the points of opposition, but I feel as though the points about time, interest, and potential annoyance weren't addressed particularly well. On top of this, many of the examples felt too complex to add to a Grades 8-12 curriculum. I myself felt dread about having to do assignments on many of the examples given. 

3) Overall, I never really thought about adding history directly to my teaching, but after this article I'm cautiously optimistic about trying it, even if I'm not as enthusiastic as I was before I read it. At the very end of the article there are some interesting ideas about ways to add history to math. I feel inspired to attempt some outdoor experiences, games, and plays for math history in my class. They all sound like the kinds of things I enjoyed as a student, and I think it would be a great way to add history into math in a fun way.

History, perhaps let's be a little silly. 

 

Welcome to the Wonderland Archives

 Hello and welcome to the trivial library of Wonderland. 

It was once great, but that no longer made sense.

You might say this library is fishy, but I assure you it's just the shrimp shaped cats.